Structured Modeling and Control of Adaptive Optics Systems

The objective of adaptive optics (AO) system control is to design an output feedback controller to reduce the adverse effect of the phase aberration caused by the atmospheric turbulence. As the size of the telescope or AO system becomes larger and larger, how to improve the efficiency of the controller execution becomes an urgent but challenging problem. To this end, this paper presents a structured and sparse controller design method for the large-scale AO systems. A Kronecker structured turbulent phase model, inspired by the frozen-flow movement of the atmospheric turbulence, is developed first, following the design of a sparse controller gain under the H2 -norm optimal control framework. Based on the Kronecker structured system matrices and the sparse controller gain, the obtained dynamical controller has a linear execution complexity in the dimension of the turbulent phase, which is even lower than the standard matrix-vector multiplication method. Since the proposed method is a preliminary result, which cannot be directly used in a telescope today, its performance is demonstrated by numerical simulations only.